Electroweak and QCD corrections to top-pair hadroproduction in association with heavy bosons

We compute the contribution of order ${\alpha }_S^2{\alpha }^2$ to the cross section of a top-antitop pair in association with at least one heavy Standard Model boson – $Z$, $W^{\pm }$, and Higgs – by including all effects of QCD, QED, and weak origin and by working in the automated MadGraph5_aMC@NLO framework. This next-to-leading order contribution is then combined with that of order ${\alpha }_S^3\alpha$, and with the two dominant lowest-order ones, ${\alpha }_S^2\alpha$ and ${\alpha }_S{\alpha }^2$, to obtain phenomenological results relevant to a 8, 13, and 100~TeV $pp$ collider.